3:00–4:00 pm Eckhart 206
Title: Conformal Dimension of Stochastic Fractals
Abstract:
The conformal dimension of a metric set is the smallest possible Hausdorff dimension among all its quasisymmetric images. Although this notion originates in geometric analysis, it has deep connections with fractal geometry, probability, and dynamics. In this talk, I will give an overview of recent results on conformal dimension for both deterministic and random fractal sets. After introducing the basic ideas and examples, I will discuss classes such as Bedford-McMullen self-affine sets and self-affine fractal percolation clusters, highlighting how geometry and randomness influence their conformal dimension. A central result of the talk is that the graph of Brownian motion is minimal: its conformal dimension equals its Hausdorff dimension, which is 3/2. The talk is based on joint work with Hrant Hakobyan (Kansas State University) and Wenbo Li (Tsinghua University).